Books relevant to our class

(under construction)

Convex Analysis

1. Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal. Fundamentals of convex analysis. Springer. 2004.

2. R. Tyrrell Rockafellar. Convex analysis. Princeton University Press. 1970

3. Dimitri Bertsekas.

4. Constantin Niculescu and Lars-Erik Persson. Convex functions and their applications. Canadian Mathematical Society. 2006

5. Jonathan Borwein and Adrian Lewis. Convex Analysis and Nonlinear Optimization. Canadian Mathematical Society. 2006

6. Lars Hörmander. Notions of convexity. Modern Birkhäuser Classics. 2007

7. A. Wayne Roberts, Dale E. Varberg. Convex functions. Academic Press UK. 1973

Convex Optimization

1. Yurii Nesterov. Introductory lectures on convex optimization. Kluwer-Academic. 2003

2. Yurii Nesterov, Arkadii Nemirovskii. Interior-Point Polynomial Algorithms in Convex Programming. SIAM. 1994

3. Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal. Convex Analysis and Minimization Algorithms, vols I, II. Springer-Verlag. 1993.

4. Alexander Shapiro, Arkadii Nemirovskii. Lectures on modern convex optimization. SIAM

5. Stephen Boyd, Lieven Vandenberghe. Convex Optimization. Cambridge University Press. 2003.

6. Suvrit Sra, Sebastian Nowozin, Stephen Wright (eds). Optimization for Machine Learning. MIT Press. 2011

Nonlinear programming

1. Dimitri Bertsekas. Nonlinear programming. Athena Scientific. 1999

2. Jorge Nocedal, Stephen J. Wright. Numerical optimization.

Convex geometry and optimization

1. Branko Grünbaum. Convex Polytopes. GTM 221. 2003 (second edition).

2. Grigoriy Blekherman, Pablo A. Parrilo, Rekha Thomas. Semidefinite Optimization and Convex Algebraic Geometry. MPS-SIAM Series (Book 13). 2012

3. Jesus A. De Loera, Raymond Hemmecke and Matthias Koeppe. Algebraic and Geometric Ideas in the Theory of Discrete Optimization. MPS-SIAM Series (Book 14). 2012.

Math (metric spaces, geometry, analysis, etc.)

1. Martin R. Bridson André Haefliger. Metric Spaces of Non-Positive Curvature. Springer-Verlag. 1999

2. Athanase Papadopoulos. Metric Spaces, Convexity and Nonpositive Curvature. European Mathematical Society. 2005

3. Lindenstrauss. Geometric nonlinear functional analysis

4. Jacques Faraut, Adam Korányi. Analysis on Symmetric Cones. Caldrendon Press. 1994

Matrix analysis

1. Horn and Johnson.

2. Rajendra Bhatia. Matrix Analysis. Springer GTM 169. 1997

3. Rajendra Bhatia. Positive definite matrices. Princeton University Press. 2007

4. Richard Bellman. Introduction to matrix analysis. SIAM

5. Fuzen Zhang.

6. Denis Serre. Matrices. Springer GTM. 2012 (second edition)

Fixed-point theory

1. Granas and Dugundi. Fixed point theory.

2. Mohamed A. Khamsi, William A. Kirk. An introduction to metric spaces and fixed point theory. John Wiley & Sons. 2001.

Miscellaneous

1. Marshall, Olkin, Arnold. Inequalities: Theory of Majorization and its Applications.

2. Hardy, Littlewood, Poly'a. Inequalities.

3. Berg, Christensen, Ressel. Harmonic analysis on semigroups.

4. R. Tyrrell Rockafellar, Roger J-B Wets. Variational Analysis. Springer. 2009 edition